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The Islamic University of Gaza Faculty of

Engineering Civil Engineering Department

Hydraulics - ECIV 3322

Chapter 4

Unsteady Flow in Pipes

Water Hammer Phenomenon in pipelines

- A sudden change of flow rate in a large pipeline

(due to valve closure, pump turnoff, etc.) may

involve a great mass of water moving inside the

pipe. - The force resulting from changing the speed of

the water mass may cause a pressure rise in the

pipe with a magnitude several times greater than

the normal static pressure in the pipe. - The excessive pressure may fracture the pipe

walls or cause other damage to the pipeline

system. - This phenomenon is commonly known as the water

hammer phenomenon

Some typical damages

Burst pipe in power sation Big Creek 3, USA

Pump damage in Azambuja Portugal

Pipe damage in power station Okigawa

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Water Hammer

- Consider a long pipe AB
- Connected at one end to a reservoir containing

water at a height H from the center of the pipe. - At the other end of the pipe, a valve to regulate

the flow of water is provided.

- If the valve is suddenly closed, the flowing

water will be obstructed and momentum will be

destroyed and consequently a wave of high

pressure will be created which travels back and

forth starting at the valve, traveling to the

reservoir, and returning back to the valve and so

on. - This wave of high pressure
- Has a very high speed (called celerity, C )

which may reach the speed of sound wave and may

create noise called knocking, - Has the effect of hammering action on the walls

of the pipe and hence is commonly known as the

water hammer phenomenon.

- The kinetic energy of the water moving through

the pipe is converted into potential energy

stored in the water and the walls of the pipe

through the elastic deformation of both. - The water is compressed and the pipe material is

stretched. - The following figure illustrates the formation

and transition of the pressure wave due to the

sudden closure of the valve

Propagation of water hammer pressure wave

Steady state condition

Transient condition t lt L/C

Transient condition t L/C

Transient condition L/C gtt gt2L/C

Transient condition t 2L/C

Transient condition 2L/C gtt gt3L/C

Transient condition t 3L/C

Transient condition 3L/C gtt gt4L/C

Transient condition t 4L/C

Analysis of Water Hammer Phenomenon

- The pressure rise due to water hammer depends

upon - (a) The velocity of the flow of water in pipe,
- (b) The length of pipe,
- (c) Time taken to close the valve,
- (d) Elastic properties of the material of the

pipe. - The following cases of water hammer will be

considered - Gradual closure of valve,
- Sudden closure of valve and pipe is rigid, and
- Sudden closure of valve and pipe is elastic.

- The time required for the pressure wave to travel

from the valve to the reservoir and back to the

valve is - Where
- L length of the pipe (m)
- C speed of pressure wave, celerity (m/sec)
- If the valve time of closure is tc , then
- If the closure is considered gradual
- If the closure is considered sudden

- The speed of pressure wave C depends on
- the pipe wall material.
- the properties of the fluid.
- the anchorage method of the pipe.
- if the pipe is rigid
- if the pipe is elastic
- and

- Where
- C velocity (celerity) of pressure wave due to

water hammer. - water density ( 1000 kg/m3 ).
- Eb bulk modulus of water ( 2.1 x 109 N/m2 ).
- Ec effective bulk modulus of water in elastic

pipe. - Ep Modulus of elasticity of the pipe

material. - e thickness of pipe wall.
- D diameter of pipe.
- K factor depends on the anchorage method
- for pipes free to move longitudinally,
- for pipes anchored at both ends against

longitudinal movement - for pipes with expansion joints.
- where poissons ratio of the pipe

material (0.25 - 0.35). It may take the value

0.25 for common pipe materials.

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The Maximum pressure created by the water hammer

Case 1 Gradual Closure of Valve

- If the time of closure , then the

closure is said to be gradual and the increased

pressure is - where,
- V0 initial velocity of water flowing in the

pipe before pipe closure - t time of closure.
- L length of pipe.
- water density.
- The pressure head caused by the water hammer

is

Another method for closure time (t gt 2 L/C)

Case 2 Sudden Closure of Valve and Pipe is Rigid

- If the time of closure , then the

closure is said to be Sudden. - The pressure head due caused by the water hammer

is - But for rigid pipe so

Case 3 Sudden Closure of Valve and Pipe is

Elastic

- If the time of closure , then the

closure is said to be Sudden. - The pressure head caused by the water hammer is
- But for elastic pipe so

Water hammer pressure head

- Applying the water hammer formulas we can

determine the energy gradient line and the

hydraulic gradient line for the pipe system under

steady flow condition.

Due to water hammer

HA

Water Hammer Pressure in a Pipeline

So the total pressure at any point M after

closure (water hammer) is

or

Time History of Pressure Wave (Water Hammer)

- The time history of the pressure wave for a

specific point on the pipe is a graph that simply

shows the relation between the pressure increase

( ) and time during the propagation of the

water hammer pressure waves.

- For example, considering point A just to the

left of the valve. - Note friction (viscosity) is neglected.

1

Time history for pressure at point A (after

valve closure)

The time history for point M (at midpoint of

the pipe)

1

Note friction (viscosity) is neglected.

The time history for point B (at a distance x

from the reservoir )

t(2L/C)

1

Note friction (viscosity) is neglected.

This is a general graph where we can substitute

any value for x (within the pipe length) to

obtain the time history for that point.

In real practice friction effects are considered

and hence a damping effect occurs and the

pressure wave dies out, i.e. energy is

dissipated.

Damping effect of friction

t(2L/C)

the time history for pressure at point A when

friction (viscosity) is included

Stresses in the pipe wall

- After calculating the pressure increase due to

the water hammer, we can find the stresses in the

pipe wall - Circumferential (hoop) stress fc
- Longitudinal stress fL

where D pipe inside diameter tp pipe

wall thickness

total pressure initial pressure (before

valve closure) pressure increase due water

hammer.

Example 1

Solution

To keep the water hammer pressure within

manageable limits, valves are commonly design

with closure times considerably greater than 2L/C

Example

- A cast iron pipe with 20 cm diameter and 15 mm

wall thickness is carrying water from a

reservoir. At the end of the pipe a valve is

installed to regulate the flow. The following

data are available - e 0.15 mm (absolute roughness) ,
- L 1500 m (length of pipe),
- Q 40 l/sec (design flow) ,
- K 2.1 x 109 N/m2 (bulk modulus of water),
- E 2.1 x 1011 N/m2 (modulus of elasticity of

cast iron), - 0.25 (poissons ratio),
- 1000 kg/m3
- T 150 C.

- Find , , fc , and fL due

to the water hammer produced for the following

cases - Assuming rigid pipe when tc 10 seconds, and tc

1.5 seconds. - Assuming elastic pipe when tc 10 seconds, and

tc 1.5 seconds, if - the pipe is free to move longitudinally,
- the pipe is anchored at both ends and throughout

its length, - the pipe has expansion joints.
- Draw the time history of the pressure wave for

the case (b-3) at - a point just to the left of the valve, and
- a distance x 0.35 L from the reservoir.
- Find the total pressure for all the cases in

(b-3).